Methods of heating ions in a plasma



June 21, 1966 S. M. HAMBERGER METHODS OF HEATING IONS IN A PLASMA FiledAug. 21, 1963 United States Patent O METHODS F HEATING IONS IN A PLASMASydney kMaxwell Hamberger, Abingdon, England, as-

signor to United Kingdom Atomic Energy Authority,

London, England Filed Aug. 21, 1963, Ser. No. 303,606 Claims priority,application Great Britain, Aug. 24, 1962,

32,531/ 62 2 Claims. (Cl. 176--3) This invention relates `to methods ofheating ions in a plasma.

The electrons in a plasma contained by a magnetic field can readily beheated by feeding in electromagnetic waves of frequency equal to theelectron cyclotron frequency. Heating the ions in a plasma by feeding insuch energy at the ion cyclotron frequency is, however, more difficult,asin most pratical cases the ion cyclotron frequency is so much lowerthan the plasma frequency that electromagnetic Waves of frequency equalto the ion cyclotron frequency wave may not penetrate the plasmasufciently to effect useful heating of the ions.

According to the present invention the ions in a plasma contained by amagnetic field are heated by subjecting the plasma to twoelectromagnetic waves each of a frequency l high enough :to penetratethe plsama effectively and dif- A method in accordance with thepresent'invention for l heating ions in a plasma will now be describedby way of example with reference to the accompanying drawing. Thedrawing shows diagrammatically an experimental apparatus in which themethod has been carried out.

The apparatus comprises a cavity 1 of circular crosssection at the endsof which are coils 2 which when energised from a direct current source(not shown) produce a magnetic field within the cavity 1. This field isindicated by the dotted lines 3 and is substantially uniform over thecentral portion of the length of the cavity 1, but is constrictedtowards the ends. The cavity 1 contains hydrogen or helium maintained ata low pressure by a pumping arrangement 4.

The apparatus also includes two klystron oscillators 5 and 6 which arearranged to generate two sinusoidal electromagnetic waves and to supplythem to the cavity 1 by way of a common path which includes a broadband, high power, klystron amplifier 7, a tuning device 8, and awaveguide 9. The tuning device -8 is used for matching purposes.

Projecting into the cavity 1 is a probe 10 which includes a small coil11. During operation a voltage is induced in the coil 11 in dependenceupon the rate of change of theaxial magnetic field in the cavity 1, andthis voltage, after amplification by an amplifier 12, is displayed on anoscilloscope 13.

The method of operation is as follows. At the centre of the caviety 1the magnetic field is approximately 3 kilogauss and the electroncyclotron frequency of the plasma contained by this field is thereforeapproximately 9400 megacyclesper second, at which frequency the cavity 1is arranged to resonate. y

3,257,283 Patented June 21, 1966 ICC The electromagnetic waves producedby the oscillators 5 and 6 both have a frequency approximately equal tothe electron cyclotron frequency, but the difference in the twofrequencies is variable over a range' of about 0.5 to megacyclespersecond. These two electromagnetic waves, which are sup-plied to thecavity 1 over the waveguide 9, are able to penetrate the plasma. Theplasma acts as a non-linear impedance and generates within itselfelectromagnetic waves at the sum and difference frequencies. It is` tobe expected that when the difference frequency is at least approximatelyequal to the ion cyclotron frequency the electromagnetic waves at thedifference frequency will resonate with the ion motions and heating ofthe ions will result. f

The amplifier 12 responds to the difference frequency and therefore theamplitude of the voltage supplied by the amplifier 12 is a measure ofthe amplitude of electromagnetic waves of .this frequency in theplsamaproduced by the non-linear coupling of the two high frequencyelectromagnetic Waves.

If readings are taken of this amplitude for a range of differencefrequencies and the readings plotted against4 the magnitude of thedifference frequency, it is found that there is a dip in the curve inthe region where the difference frequency is equal to the ion cyclotron.frequency in the mid-plane. This finding is consistent with thesupposition that at that difference frequency the ions are being heated,with a consequent lossof energy by the electromagnetic waves having thedifference frequency.

One suggested explanation of the mechanism, the explanation beingsimplified and ignoring the effect of collisions, is as follows. In theinterior of a plasma the magnetic field is less than the appliedmagnetic field, due

. to the field resulting fromgyration of the charged particles .aroundthe magnetic field lines. This effect is directly proportional to thesummation of the energy of the particles transverse to the appliedmagnetic field. If the transverse energy of the particles fiuctuates,therefore, the internal magnetic field will fluctuate.

Thus if the electrons are additionally subjected to two sinu-soidallyvarying electric fields having frequencies just above and below thenatural frequency of rotation (the electron cyclotron frequency), theelectrons will execute oscillating spirals, the radii of which will varyat the difference'frequency. Thatis to say, the energy of the electronstransverse to the magnetic field varies at the difference frequency. Anoscillatory magnetic eld is therefore produced within the plasma in thesame direction and opposite to the applied field. This oscillatorymagnetic field has associated with it an azimuthal electric field at thedifference frequency which can couple to the lons.

Other known methods of generating the -two electromagnetic waves lmay beused, and the waves may then be supplied over the same or separate pathsto the cavity 1.

The method is not restricted to heating of ions in a mirror field, butcan be applied to any containment geometry in which there is anessentially uniform region of magnetic field.

I claim:

1. In a method of heating ions in a plasma having an ion cyclotronfrequency and contained by a magnetic field, the steps of subjecting theplasma to two radio frequency electromagnetic waves each of a frequencyhigh enough to penetrate effectively the plasma, said waves differing bya frequency which resonates with the ion cyclotron frequency.

2. In a method of heating ions in a plasma having an ion cyclotronfrequency and an electron cyclotron frequency with said plasma beingcontained by a magnetic field, the steps of subjecting the plasma to tworadio frequency electromagnetic waves each of a frequency approximatelyequal to the electron cyclotron frequency, said waves diiering by afrequency approximately equal to the ion cyclotron frequency.

References Cited by the Examiner UNITED STATES PATENTS Spencer 219-1055Kamide 219--l0.55

Chang 313-161 Herold 313-161 3,090,737 5/1963 Swartz 313-161 3,104,3059/1963 Crapuchettes 219-1055 3,105,803 10/1963 Weibel 313-161 L. H.BENDER, Assistant Examiner.

1. IN A METHOD OF HEATING IONS IN A PLASMA HAVING AN ION CYCLOTRONFREQUENCY AND CONTAINED BY A MAGNETIC FIELD, THE STEPS OF SUBJECTING THEPLASMA TO TWO RADIO FREQUENCY ELECTROMAGNETIC WAVES EACH OF A FREQUENCYHIGH ENOUGH TO PENETRATE EFFECTIVELY THE PLASMA,SAID WAVES DIFFERING